# capacitor question help

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A capacitor is discharging though a resistor and the time constant is 5.0 s. The time taken for the capacitor to lose half its charge is ?

My answer is 0.14s but the mark scheme said that the answer should be 3.5 s?!

My answer is 0.14s but the mark scheme said that the answer should be 3.5 s?!

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#3

(Original post by

A capacitor is discharging though a resistor and the time constant is 5.0 s. The time taken for the capacitor to lose half its charge is ?

My answer is 0.14s but the mark scheme said that the answer should be 3.5 s?!

**Lamalam**)A capacitor is discharging though a resistor and the time constant is 5.0 s. The time taken for the capacitor to lose half its charge is ?

My answer is 0.14s but the mark scheme said that the answer should be 3.5 s?!

ke

^{-t/CR}

i.e:

when t = CR (t= 5.0 seconds)

-t/CR = -1

then e

^{-}

^{t/CR }e

^{-t/5}= e

^{-}

^{1}= 0.3679

i.e. charge or voltage on the capacitor has fallen to approx' 37% of its original value.

The question is asking for the time t such that e

^{-t/5}= 0.5

Can you solve this now?

HINT. Use natural logs

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(Original post by

The charge on the capacitor is given by the relationship

ke

i.e:

when t = CR (t= 5.0 seconds)

-t/CR = -1

then e

i.e. charge or voltage on the capacitor has fallen to approx' 37% of its original value.

The question is asking for the time t such that e

Can you solve this now?

HINT. Use natural logs

**uberteknik**)The charge on the capacitor is given by the relationship

ke

^{-t/CR}i.e:

when t = CR (t= 5.0 seconds)

-t/CR = -1

then e

^{-}^{t/CR }e^{-t/5}= e^{-}^{1}= 0.3679i.e. charge or voltage on the capacitor has fallen to approx' 37% of its original value.

The question is asking for the time t such that e

^{-t/5}= 0.5Can you solve this now?

HINT. Use natural logs

thank you !

I calculated the wrong answer at first because I think the time required is actually the HALF LIVE . And then I use half live = ln 2 / RC to get the answer. why the time isn't half lives?

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#5

(Original post by

Take the natural log of both sides of the equation and rearrange to get t=3.47 s --> 3.5s

thank you !

I calculated the wrong answer at first because I think the time required is actually the HALF LIVE . And then I use half live = ln 2 / RC to get the answer. why the time isn't half lives?

**Lamalam**)Take the natural log of both sides of the equation and rearrange to get t=3.47 s --> 3.5s

thank you !

I calculated the wrong answer at first because I think the time required is actually the HALF LIVE . And then I use half live = ln 2 / RC to get the answer. why the time isn't half lives?

e

^{-lambda x t}

However, don't mix the two because the examiner will award marks for the correct use of e

^{-t}

^{/CR}and none if you used your method which produced the wrong result.

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(Original post by

You can but you would need to use (RC)ln2 since with half lives, the relationship is

e

However, don't mix the two because the examiner will award marks for the correct use of e

**uberteknik**)You can but you would need to use (RC)ln2 since with half lives, the relationship is

e

^{-lambda x t}However, don't mix the two because the examiner will award marks for the correct use of e

^{-t}^{/CR}and none if you used your method which produced the wrong result.e

^{-lambda x t}is applicable in this question? I thought this equation can only be used in the radioactivity-related question? if it can be used in the question, what would lambda represents?

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#7

(Original post by

silly me ! I rmb the equations wrongly .

e

**Lamalam**)silly me ! I rmb the equations wrongly .

e

^{-lambda x t}is applicable in this question? I thought this equation can only be used in the radioactivity-related question? if it can be used in the question, what would lambda represents?As I said, don't mx them up, it only serves to confuse.

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(Original post by

Not really since lambda is the time taken for 50% of the atoms to decay whereas CR is the time for the charge to fall to 37%

As I said, don't mx them up, it only serves to confuse.

**uberteknik**)Not really since lambda is the time taken for 50% of the atoms to decay whereas CR is the time for the charge to fall to 37%

As I said, don't mx them up, it only serves to confuse.

Thank you very much!

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#9

(Original post by

If the decay constant is 4.30*10^-4 year^-1, what does it mean? I couldn't associate the 50% with 4.30*10^-4 year^-1.

Thank you very much!

**Lamalam**)If the decay constant is 4.30*10^-4 year^-1, what does it mean? I couldn't associate the 50% with 4.30*10^-4 year^-1.

Thank you very much!

Your statement states a quantity of something is decaying at given rate without stating the original quantity. Can you post the original question please?

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(Original post by

Half life decay is stated as a time. Meaning half of the original quantity will decay within the time period.

Your statement states a quantity of something is decaying at given rate without stating the original quantity. Can you post the original question please?

**uberteknik**)Half life decay is stated as a time. Meaning half of the original quantity will decay within the time period.

Your statement states a quantity of something is decaying at given rate without stating the original quantity. Can you post the original question please?

I think I mix up half life and decay constant? Are they the same thing ?

Posted from TSR Mobile

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#11

(Original post by

I think I mix up half life and decay constant? Are they the same thing ?

Posted from TSR Mobile

**Lamalam**)I think I mix up half life and decay constant? Are they the same thing ?

Posted from TSR Mobile

One refers to an actual physical quantity (rate of change of charge) and the other is the probability of a rate of decay occurring in the stated time.

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(Original post by

No. The equations look similar but re not the same.

One refers to an actual physical quantity (rate of change of charge) and the other is the probability of a rate of decay occurring in the stated time.

**uberteknik**)No. The equations look similar but re not the same.

One refers to an actual physical quantity (rate of change of charge) and the other is the probability of a rate of decay occurring in the stated time.

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#13

(Original post by

but then lambda is not the time taken for 50% of the atoms to decay , but half life does? Thank you for answering my question!

**Lamalam**)but then lambda is not the time taken for 50% of the atoms to decay , but half life does? Thank you for answering my question!

So e

^{-t/CR}has the same form as e

^{-lambda * t}

1/CR = 1/ tor since the product of the dimensions for Farrads and Ohms = seconds

lambda = k/tor = k(1/tor) where k is a property of the atomic element

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